This paper presents a complete analytical framework for modeling memoryless nonlinear effects in an intensity modulation and direct detection optical wireless communication system based on orthogonal frequency division multiplexing. The theory employs the Bussgang theorem, which is widely accepted as a means to characterize the impact of nonlinear distortions on normally distributed signals. This paper proposes a new method to generalize this approach, and it describes how a closed-form analytical expression for the system bit error rate can be obtained for an arbitrary memoryless distortion. Major distortion effects at the transmitter stage such as quantization and nonlinearity from the light emitting diode are analyzed. Four known orthogonal-frequency-division-multiplexing-based modulation schemes for optical communication are considered in this paper: direct-current-biased optical OFDM, asymmetrically clipped optical OFDM, pulse-amplitude-modulated discrete multitone modulation, and unipolar orthogonal frequency division multiplexing.